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8
P
compactnessintermsofflters,asgivenin[Na1],[JN2]and[JKN2]
facilitatedthestudyoftheseclassesofspacesinthisunifyingoperator
approach.
Chapter6pointsoutsomeapplicationsoftheadherencedomina-
toroperator.Someoftheapplicationsofthisoperatoraregivenin
Section4.5.Throughouteachofthechapters,whenatheoremisstated
intermsoftheadherencedominator,acorollaryfollowswherethe
resultisstatedwiththespecificadherencerelevanttotheresult.Some
ofsuchcasesfromChapter5arepointedoutinChapter6toillustrate
theapplicationsoftheoperator.Alsosomemorerecentresultsfrom
[EJKN4]areexplicitlystatedtofurtherillustratethisaspectofthe
opeartor.
Thisstudyofgeneraltopologicalpropertieswithaunifyingop-
eratorwillprovidemoreinsightandmotivatereaderstoinvestigate
othertopologicalpropertieswithsimilartools.Lookingatallthose
propertieswhichhavecommontrendofbehaviourisfascinating.Such
investigativeapproachwillexpandthehorizonandscopeofthesub-
jectaswell.
Alistofnotationsusedisprovided.Thisisdonesincesomeof
thenotationsusedarespecificandmightnotbegenerallyrecognized.
Theseareadaptedtoavoidrepeatationsofstatements.
Theauthorsverymuchappreciateconstructivecommentsand
meticulouseditingoftheoriginalsubmissionofthismonographby
thereviewers.Severalmodificationsaremadetakingtheirsugges-
tionsunderconsideration.OnesignificantadditionistheChapter6,
ApplicationsoftheAdherenceDominator.Moredetailsaregivenin
Chapter3onConnectednessandeachchapterisdividedintoseve-
ralsections.Somemorerecentresultsbytheauthorsareaddedin
Chapters4and5.
WeacknowledgethetimereleasereceivedfromMorganState
UniversityforBhaminiNayarintheformofsabbaticalleaveforthe
Spring2020semester.Wehadreceivedtheapprovalfortheproposal
towritethismonographacoupleofyearsago.However,wehadto
waitfortherelease-timeforasemestertohaveuninterruptedtimeto
completethis.WeappreciateDr.ZeinabBandpey’shelpinputting
